The term "mimosa" is most often associated with the drink made from orange juice and Champagne. But a garnish using a hard-cooked egg yolk, such as in the dressing for this sandwich, is also referred to as mimosa.
Combine the first 9 ingredients in a large bowl; add chopped arugula and romaine lettuce, tossing gently to coat.
Place 1 tomato slice in each pita half; divide cucumber slices evenly among pita halves. Place about 1/4 cup arugula mixture in each pita half.